Introduction

Nesting Phenology

Climatology plot

Linear mixed-effects with turtle-level and year-level hierarchical intercepts

stan_lmer
 family:       gaussian [identity]
 formula:      doy_encounter ~ (1 | name) + (1 | fyear)
 observations: 1813
------
            Median MAD_SD
(Intercept) 129.8    1.0 

Auxiliary parameter(s):
      Median MAD_SD
sigma 21.5    0.4  

Error terms:
 Groups   Name        Std.Dev.
 name     (Intercept)  7.3    
 fyear    (Intercept)  3.1    
 Residual             21.5    
Num. levels: name 567, fyear 14 

------
* For help interpreting the printed output see ?print.stanreg
* For info on the priors used see ?prior_summary.stanreg

Linear mixed-effects with turtle-level and year-level hierarchical intercepts and a linear time trend

stan_lmer
 family:       gaussian [identity]
 formula:      doy_encounter ~ year_ctr + (1 | name) + (1 | fyear)
 observations: 1813
------
            Median MAD_SD
(Intercept) 129.8    1.1 
year_ctr     -0.1    0.2 

Auxiliary parameter(s):
      Median MAD_SD
sigma 21.5    0.4  

Error terms:
 Groups   Name        Std.Dev.
 name     (Intercept)  7.3    
 fyear    (Intercept)  3.3    
 Residual             21.5    
Num. levels: name 567, fyear 14 

------
* For help interpreting the printed output see ?print.stanreg
* For info on the priors used see ?prior_summary.stanreg

Linear mixed-effects with turtle-level and year-level hierarchical intercepts and a linear time trend and weather covariates

stan_lmer
 family:       gaussian [identity]
 formula:      doy_encounter ~ year_ctr + humid_std + ws_std + p_std + t_std + 
       ppt_std + sst_std + (1 | name) + (1 | fyear)
 observations: 1813
------
            Median MAD_SD
(Intercept) 129.7    1.2 
year_ctr     -0.4    0.6 
humid_std     1.1    2.0 
ws_std       -0.4    2.5 
p_std         0.7    1.5 
t_std        -1.0    2.4 
ppt_std       0.5    2.0 
sst_std       1.2    1.4 

Auxiliary parameter(s):
      Median MAD_SD
sigma 21.5    0.4  

Error terms:
 Groups   Name        Std.Dev.
 name     (Intercept)  7.3    
 fyear    (Intercept)  4.6    
 Residual             21.5    
Num. levels: name 567, fyear 14 

------
* For help interpreting the printed output see ?print.stanreg
* For info on the priors used see ?prior_summary.stanreg

Hierarchical skew-normal model with turtle-level and year-level intercepts

 Family: skew_normal 
  Links: mu = identity; sigma = identity; alpha = identity 
Formula: doy_encounter ~ (1 | name) + (1 | fyear) 
   Data: turtle (Number of observations: 1813) 
Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup samples = 3000

Group-Level Effects: 
~fyear (Number of levels: 14) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     2.83      1.03     1.06     5.18 1.00      871     1158

~name (Number of levels: 567) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     6.45      1.10     4.20     8.40 1.00      465      502

Population-Level Effects: 
          Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept   129.91      1.06   127.74   131.96 1.00     1267     1584

Family Specific Parameters: 
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma    21.94      0.52    20.99    22.97 1.00     1043     1169
alpha    -2.06      0.46    -3.03    -1.19 1.00     1681     1893

Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Hierarchical skew-normal model with turtle-level intercept and year-level intercept, dispersion and skew

 Family: skew_normal 
  Links: mu = identity; sigma = identity; alpha = identity 
Formula: doy_encounter ~ (1 | name) + (1 | fyear) 
         alpha ~ (1 | fyear)
   Data: turtle (Number of observations: 1813) 
Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup samples = 3000

Group-Level Effects: 
~fyear (Number of levels: 14) 
                    Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)           2.91      1.04     1.22     5.31 1.00     1029     1410
sd(alpha_Intercept)     2.56      1.19     0.86     5.41 1.00      854     1361

~name (Number of levels: 567) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     5.71      1.04     3.57     7.63 1.01      530      973

Population-Level Effects: 
                Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept         130.06      1.09   128.00   132.31 1.00     1641     1688
alpha_Intercept    -2.68      0.95    -4.78    -1.06 1.00     1508     1647

Family Specific Parameters: 
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma    22.23      0.48    21.30    23.18 1.00     1320     2200

Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Model selection using LOO

          elpd_diff se_diff elpd_loo se_elpd_loo p_loo se_p_loo looic se_looic
sn_doy1        0.00    0.00    -8203        23.7   120     4.07 16406     47.3
sn_doy0       -4.55    4.09    -8208        23.7   127     3.54 16415     47.5
lmer_doy1     -6.07    7.22    -8209        23.6   138     3.54 16419     47.2
lmer_doy0     -6.54    7.25    -8210        23.6   138     3.55 16419     47.2
lmer_doy2     -7.69    7.38    -8211        23.7   141     3.62 16422     47.3

Plot posterior predictive distribution from “full” skew-normal model and compare to data and empirical density for each year

Plot time series of encounter DOY for individual females

Plot posterior distribution of the average encounter DOY in an average year (i.e., setting all other fixed and random effects to zero) for just those females that have been seen in at least 4 years (so their random effects are relatively well identified). The lines are the posterior means. They range from late April to late May, so not a ton of variation, but individual females do seem to have distinct seasonal modes.

Somatic Growth

Hierarchical von Bertalanffy model with turtle-level and year-level \(K\) and global \(L_{\infty}\)

 Family: gaussian 
  Links: mu = identity; sigma = identity 
Formula: ccl_max ~ ccl_max0 + (exp(logLinf) - ccl_max0) * (1 - inv_logit(logitK)^dyear) 
         logitK ~ (1 | name) + (1 | fyear)
         logLinf ~ 1
   Data: size (Number of observations: 324) 
Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup samples = 3000

Group-Level Effects: 
~fyear (Number of levels: 10) 
                     Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(logitK_Intercept)     0.50      0.16     0.27     0.90 1.00      919     1346

~name (Number of levels: 207) 
                     Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(logitK_Intercept)     0.55      0.08     0.38     0.72 1.00      431      699

Population-Level Effects: 
                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
logitK_Intercept      3.83      0.24     3.35     4.31 1.00      888     1395
logLinf_Intercept     5.17      0.02     5.14     5.21 1.00     1473     1695

Family Specific Parameters: 
      Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma     1.48      0.08     1.33     1.66 1.00      573     1364

Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Plot individual growth trajectories. A few females shrank considerably while others grew much faster than average.

Plot von Bertalanffy growth curves (hyper-mean and female-specific) with data overlay

Proportion of Neophytes

Fit intercept-only binomial GLM

stan_glm
 family:       binomial [logit]
 formula:      cbind(neophyte, remigrant) ~ 1
 observations: 14
 predictors:   1
------
            Median MAD_SD
(Intercept) -0.58   0.06 

------
* For help interpreting the printed output see ?print.stanreg
* For info on the priors used see ?prior_summary.stanreg

Fit binomial GLM with time trend

stan_glm
 family:       binomial [logit]
 formula:      cbind(neophyte, remigrant) ~ year_ctr
 observations: 14
 predictors:   2
------
            Median MAD_SD
(Intercept) -0.70   0.07 
year_ctr    -0.12   0.02 

------
* For help interpreting the printed output see ?print.stanreg
* For info on the priors used see ?prior_summary.stanreg

Model comparison using LOO

         elpd_diff se_diff elpd_loo se_elpd_loo p_loo se_p_loo looic se_looic
glm_neo1       0.0     0.0    -49.1        6.95  3.67     1.11  98.2     13.9
glm_neo0     -26.6     9.5    -75.7        9.03  5.72     1.55 151.4     18.1

Plot fitted relationship and PPD along with data and sample confidence intervals

Emergence Success

Zero-inflated binomial models [explain ZIB using example from full model]

Full model fitted to all nests. Binomial component: year-level hierarchical intercept, nest- (observation-) level overdispersion residual, linear time trend, fixed effects of beach, distance to HWL and distance to dune. Zero-inflated component: fixed effects of distance to HWL and distance to dune.

 Family: zero_inflated_binomial 
  Links: mu = logit; zi = logit 
Formula: emerged | trials(clutch) ~ year_ctr + beach + dist_hwl_std + dist_dune_std + (1 | fyear) + (1 | nestID) 
         zi ~ dist_hwl_std + dist_dune_std
   Data: nest (Number of observations: 2178) 
Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup samples = 3000

Group-Level Effects: 
~fyear (Number of levels: 14) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.64      0.16     0.41     1.02 1.00      484      955

~nestID (Number of levels: 2178) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     1.43      0.03     1.38     1.48 1.00      271      663

Population-Level Effects: 
                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept           -0.45      0.23    -0.91     0.04 1.01      195      329
zi_Intercept        -2.62      0.09    -2.81    -2.44 1.00     2593     2153
year_ctr            -0.03      0.04    -0.12     0.05 1.01      425      765
beachJC              0.64      0.16     0.31     0.94 1.01      178      315
beachJB              0.38      0.15     0.05     0.67 1.01      139      189
dist_hwl_std        -0.06      0.03    -0.12     0.00 1.01      162      358
dist_dune_std        0.01      0.04    -0.06     0.07 1.02       89      214
zi_dist_hwl_std     -0.40      0.11    -0.63    -0.17 1.00     1803     2125
zi_dist_dune_std     0.16      0.08     0.00     0.31 1.00     2899     2511

Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).

Plot probability of nest failure vs. distance from HWL and dune

Plot overall emergence rate vs. distance from HWL and dune

Full model fitted to only nests associated with an encounter. Binomial component: year-level and turtle-level hierarchical intercepts, nest- (observation-) level overdispersion residual, linear time trend, fixed effects of beach, distance to HWL and distance to dune. Zero-inflated component: fixed effects of distance to HWL and distance to dune.

 Family: zero_inflated_binomial 
  Links: mu = logit; zi = logit 
Formula: emerged | trials(clutch) ~ year_ctr + beach + dist_hwl_std + dist_dune_std + neophyte + (1 | fyear) + (1 | name) + (1 | nestID) 
         zi ~ dist_hwl_std + dist_dune_std
   Data: subset(nest, beach != "TEQ") (Number of observations: 1428) 
Samples: 3 chains, each with iter = 2000; warmup = 1000; thin = 1;
         total post-warmup samples = 3000

Group-Level Effects: 
~fyear (Number of levels: 14) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.76      0.19     0.48     1.24 1.00     1432     2047

~name (Number of levels: 529) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     0.51      0.07     0.36     0.64 1.01      225      279

~nestID (Number of levels: 1428) 
              Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept)     1.32      0.04     1.25     1.39 1.00      639     1310

Population-Level Effects: 
                  Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept             0.06      0.24    -0.42     0.55 1.00     1823     2098
zi_Intercept         -2.59      0.11    -2.81    -2.37 1.00     3268     2730
year_ctr             -0.05      0.05    -0.16     0.05 1.00     2058     1694
beachJB              -0.18      0.12    -0.40     0.05 1.01     1643     2142
dist_hwl_std         -0.07      0.04    -0.15     0.01 1.00     1552     2066
dist_dune_std         0.08      0.04    -0.00     0.16 1.00     1555     1840
neophyteremigrant     0.01      0.09    -0.17     0.20 1.00     1664     1938
zi_dist_hwl_std      -0.44      0.13    -0.71    -0.19 1.00     3044     2733
zi_dist_dune_std      0.15      0.09    -0.05     0.32 1.00     4879     2306

Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).